This is a geometric representation of what a logarithm does. For the two equations
- y is the total distance of the line segment, which can be adjusted by moving point B
- b is the base, the proportion or constant
- x=b-1 which is the number of times b is multiplied or divided

Consider the following questions:
Do the points change when the distance is adjusted?
What happens to the points as b, the base, increases? As b decreases?
Move the slider to b=1. What happens to the points? Why?
What is the algebraic equivalent of this operation?
Move the slider to b=0. What happens to the points? Why?
Compare the x-coordinates of the points when b=2 and b=10. How would you describe the sequence of numbers?